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see explanation

Step-by-step explanation:

Given

y = (x - 1)(x - 3)

(a)

To find the x- intercepts A and B let y = 0 , that is

(x - 1)(x - 3) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 3 = 0 ⇒ x = 3

Thus A = (1, 0 ) and B = (3, 0 )

(b)

To find the y- intercept let x = 0, that is

y = (0 - 1)(0 - 3) = - 1 × - 3 = 3

Thus P = (0, 3 )

(c)

The x- coordinate is at the midpoint of the x- intercepts, that is

x = = = 2

Substitute this value into the equation for corresponding y- coordinate

y = (2 - 1)(2 - 3) = 1 × - 1 = - 1

Thus Q = (2, - 1 )

this answer is !